Assigning probability to output of a ReLU network
I would just skip the sigmoid function step.

Consider these two scenarios with three choices with the associated values:
0.1,10,100 or 1,100,1000
Given that these scenarios are equivalent in their relativ values, your probabilities should be assigned in the same way. But if you throw in a sigmoid function, the difference between 10 and 100 will be bigger than between 100 and 1000. 

Just normalise the values, so that they sum to 1. In that case the choice with a value ten times higher than the value of another choice will be picked ten times as often. Makes sense to me.